Parallel kinematics mechanism with a concentric sperical joint

ABSTRACT

A parallel kinematics mechanism is provided for uses such as robotics or machining. The mechanism has various limbs, at least some of which are actuatable, for moving an end component with multiple degrees of freedom. The mechanism advantageously facilitates a closed-form solution for the forward kinematics. A joint assembly is provided for use in the parallel kinematics mechanism, the joint assembly having a plurality of revolute joints for connecting to at least three limbs, the joints having non-parallel axes, which intersect at a common point. In various embodiments of the invention, the end component has three, four, five and six degrees of freedom.

The present invention generally relates to an apparatus for positioningand orienting a member in space and to joints for linking limbs of suchan apparatus.

BACKGROUND

A need exists for simple and effective parallel kinematics mechanisms.Kinematics mechanisms are used in mechanical engineering applicationsfor machining, robotics, positioning devices, coordinate measuring,fixtures and so on. In general, mechanisms can typically be classifiedas either serial or parallel. Serial kinematics mechanisms are widelyused and presently dominate the market.

A serial kinematics mechanism has a series of cantilever beams that aremovably connected together in an end-to-end fashion by prismatic,revolute or spherical joints, forming an open loop. The closer that amember is to a base of the mechanism within the serial structure, thehigher the load on that member. Additionally, the farther that a memberis from the base, the higher its deflection with respect to the basemember. When a serial kinematics mechanism is subjected to loading, theposition of the farthest member, i.e., the end-effector, is subject tothe cumulative deflections of all serial members. Unfortunately, thisresults in large positioning errors at the end-effector. Beingconstructed of cantilevers, a serial mechanism has a poor stiffness tomass ratio, making such structures bulky in design.

Serial kinematics mechanisms allow fast and easy computation of theposition of the end-effector given the position or state of allactuators. In general, this computation is known as the forwardkinematics of a mechanism. However, determining the position or state ofall actuators given the position of the end-effector, also known as theinverse kinematics, is very difficult.

Relative to serial kinematics mechanisms, parallel kinematics mechanismstypically have an improved stiffness-to-mass ratio and better accuracy.A parallel kinematics mechanism has a plurality of links which form oneor more closed loops, the links thereby sharing the load on theend-effector. Moreover, positioning errors of actuators are divided,thereby resulting in a high accuracy of the end-effector. A well-knownparallel kinematics mechanism is the Stewart Platform which wasintroduced in 1965 and has since been the subject of extensive study andanalysis. A Stewart Platform mechanism generally includes a movableplatform which is connected to a base by six controllable links. Forexample, U.S. Pat. No. 5,656,905 discloses a general overview onmechanisms that are based on or derived from the Stewart Platform.

While parallel kinematics mechanisms can provide improved accuracy,stiffness, and high load carrying capacity, parallel mechanisms alsosuffer from significant control drawbacks. Most known parallelkinematics mechanisms have very difficult forward kinematics. Thesolutions of the forward kinematics are in the form of high-orderpolynomial equations, which do not allow closed-form solutions tocompute the end-effector position. Computationally intensive methodssuch as numerical approximations must be applied in order to calculatemultiple solutions and select the right one. In some cases, particularlyin lower degree of freedom mechanisms, closed-form solutions may exist.However, these solutions involve algebraically complex expressions withfractional powers. Moreover, many of the aforementioned parallelkinematics mechanisms require run-time collision detection between theirparallel members, further complicating the control calculations.

It has been shown that the general form of the Stewart Platform hasforty feasible solutions. For some special forms of the StewartPlatform, closed-form solutions of forward kinematics exist. In thesespecial forms, pairs of spherical joints that connect the links to baseand platform are concentric. However, the difficulty of manufacturingsuch joints is well recognized in the art.

Some efforts have been made by designing ball and socket joints, whichallow two or more links to be connected to the platform or base withindependent spherical motion about a common point. However, these jointssignificantly restrict the range of spherical motion of the attachedlinks and have a limited load carrying capacity. Moreover, fabricationof such a joint is very expensive and difficult.

Parallel kinematics mechanisms are increasingly used in machining androbotics. Several mechanisms for free-form milling have been introducedinto the market recently. Most of the known mechanisms are based on theStewart Platform and allow all six degrees of freedom. These knownStewart Platform mechanisms have limited the translational androtational motion of the end-effector. However, many applications suchas machining or assembly operations require actuation about onerotational axis with infinite or very high freedom, which is usuallyaccomplished by motors or spindles mounted on the end-effector. Thismeans that one of the actuations of these mechanisms is redundant.Because of their particular configuration, many of the aforementionedparallel kinematics mechanisms require run-time collision detectionbetween their parallel members. Further, most known parallel kinematicsmechanisms have complex polyhedral workspaces whereas engineeringapplications generally require cuboidal workspace shapes. This leads toa poor workspace utilization ratio for many parallel kinematicsmechanisms.

A need therefore exists to provide a parallel kinematics mechanism thathas simple and practical forward kinematics solutions by allowing thesolution for the end-effector position in closed-form. A need exists forsuch a mechanism that has a robust and modular design with no redundantactuators and joints.

Moreover, a need exists to provide a rigid and accurate mechanism withlarge translational and rotational motion range in a cuboidal workspace.Ideally, stiffness and accuracy properties throughout the workspace ofthe mechanism should remain constant. The configuration of the mechanismshould inherently prevent collision between its parallel members.

The present invention also relates to mechanical joints, and moreparticularly, to spherical joints used to allow spherical motion tothree or more limbs about a common point.

A variety of mechanical joints are known which allow spherical motionfor multiple limbs about a common point. Some such joints areconstructed by three hemispherical shells concentrically mounted on aball, representing an extension of a ball and socket joint. Such a jointis disclosed, for example, in U.S. Pat. No. 5,179,525. The shortcomingof this type of joint is that the spherical motion of each limb becomesincreasingly limited the greater the number of limbs connected to theball. The joint does not allow tensile loads or high forces in generaland suffers from poor rigidity and accuracy. Control of structureshaving such a joint, becomes difficult due to the non-linear nature ofthe high frictional forces produced by the preloaded ball and socketassemblies. Moreover, it is not possible to access the center of thejoint without restricting spherical motion of the limbs. Neither can thejoint be stacked to increase the number of interconnected limbs whilemaintaining concentricity.

Another joint has been made using extra yokes on a universal jointassembly, as disclosed, for example, in U.S. Pat. No. 5,797,191 and E.Fichter, A Stewart Platform-Based Manipulator: General Theory andPractical Construction, 1986, The International Journal on RoboticsResearch, Vol. 5, pp. 157-182. The mechanism allows only limitedspherical motion and involves redundant revolute joints. Due to itsasymmetric design, the joint suffers singularities in certainconfigurations. Furthermore, it cannot be stacked to increase the numberof interconnected limbs and does not allow access to the center of thejoint.

Another known joint as disclosed in U.S. Pat. No. 5,657,584, uses alarge number of elements and pins to produce spherical motion of theattached limbs. Although this type of joint can be stacked to increasethe number of interconnected limbs and allows access to the centerpoint, it requires multiple expensive revolute joints and a complexstructure. Consequently, such joint is not capable of carrying highloads and offers only limited spherical motion to its limbs.

In some joints, the limbs are not truly independent to rotate about eachother, as it should ideally be for a concentric spherical joint. Theyare constrained with spatial relationships. For example, the membersmust move on a conical surface.

In other joints, the centers of rotation of the attached limbs are notcoincident. This may cause at least two problems. Firstly, compressiveand tensile loads in the limbs cause twisting and bending moments on thejoint, and the loads are not transmitted to the other limbs as in anideal truss. Secondly, in a controlled truss structure such as parallelkinematics machines, this kind of joint results in difficult forwardkinematics that allow no closed-form solution of the end-effectorposition in general.

A need therefore exists for a joint structure that has improvedspherical motion about a point common to its interconnected limbs thanpreviously known joints. The joint should allow any configuration of itslimbs with none of the limbs hindering the motion of any other.

SUMMARY OF THE INVENTION

The present invention provides a parallel kinematics mechanism whichovercomes difficulties incurred in prior art devices. The inventionfurther includes an improved joint structure which facilitates theconstruction of such an improved kinematics mechanism by allowing threeor more axes to intersect at a point, regardless of their orientation.

An object of the invention is to provide an improved mechanism forpositioning and orienting a member in space. A more specific object ofthe invention is to provide such a mechanism which facilitatessimplified forward kinematics calculation with a closed-form solution.Yet another object is to provide such a mechanism with improvedstructural rigidity.

Advantageously, a kinematics mechanism having a design according to thepresent invention is such that the forward kinematics math is greatlysimplified. The design of the proposed mechanism reduces calculations tothe simple problem of finding the point of intersection of threespheres, which makes the forward kinematics trivial and has aclosed-form solution for the end-effector position. The closed-formsolution only involves simple algebraic expressions. According to anembodiment of the invention, the solution simplification has beenachieved by a new concentric spherical joint that allows three or morelimbs to be connected together with their longitudinal axes alwaysintersecting at a point, regardless of the orientations.

In an embodiment, the invention utilizes a concentric spherical jointsuch that the structure of the positioning mechanism resembles abi-tetrahedral configuration, giving it truss-like behavior. Thebi-tetrahedral arrangement also causes decoupling between the positionand orientation of the final member. Loads on the end-effector aregenerally distributed among all actuators which, in return, compensatefor positioning errors of the end-effector through their parallelarrangement. Thereby, the mechanism provides high stiffness andaccuracy. Due to the bi-tetrahedral configuration, no collisiondetection between parallel members is required.

Another advantage of the configuration is the high workspace volume theend-effector can reach, combined with a high dexterity throughout thisworkspace which is nearly cubical in shape. Furthermore, the positioningmechanism is able to operate at high speeds due to its parallel designand simple closed-form solution.

Work tools such as cutting tools or robot grippers can be mounted on theend-effector. In an embodiment, the work tool is powered by an actuatoror a motor that is fixed on the base and transmits its rotation on thework tool through a telescopic spline-shaft assembly. This allowsmoments acting about the longitudinal axis of the working member to bedirectly transferred to the base, relieving the overall structure of thepositioning mechanism. In another embodiment, the work tool is poweredby an actuator or a motor that is fixed on the end component.

Another advantage of the invention is that, in an embodiment, itprovides a mechanism that fixedly has a modular design that only usesfive identical actuator assemblies, two kinds of concentric sphericaljoints, a base, a motor, and a working member. The low number of partsand the usage of mostly revolute joints results in a precise andcost-efficient positioning mechanism that finds wide use in many areas.

Mechanisms according to an embodiment of the invention may be useful inmachining and robotics. In particular, the mechanism can be used forfree-form milling, assembly operations, and coordinate measuring or anyother kind of operation that requires a member to be positioned andoriented in space.

In an embodiment, another object of the invention is to provide aconcentric spherical joint that allows three or more limbs to beconnected together with their longitudinal axes always intersecting at apoint, regardless of their orientation. This joint provides advantagesover the prior art, exhibiting an improved range of spherical motionamong its joined limbs, few parts, low wear and friction, improvedrigidity, and improved accuracy. It also can sustain tensile loads,unlike some ball-and-socket joints. The proposed concentric sphericaljoint according to an embodiment of the invention advantageously has asimple and robust design, involving only a minimum number of requiredrevolute joints, providing total spherical motion to threeinterconnected limbs.

A structure can be assembled using several concentric spherical jointsaccording to an embodiment of the invention to increase the number oflimbs to any number with their longitudinal axes intersecting at acommon point. While combinations of known joints constrain the sphericalmotion range, the concentric spherical joint according to an embodimentof the invention enhances this range.

The concentric spherical joint according to an embodiment of theinvention has many applications in a wide range of engineeringdisciplines. It may be used in civil engineering for spatial trusses,space grid structures, and geodesics. When used as a joint in a parallelkinematics mechanism, the concentric spherical joint can extremelysimplify the forward kinematics and reduce the amount of necessarycomputations, allowing a parallel kinematics mechanism to operate atsignificantly higher speeds.

Additional features and advantages of the present invention aredescribed in, and will be apparent from, the detailed description of thepreferred embodiments and from the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The following is a description, by way of example only, of differentembodiments of the mechanism, its variations, derivations andreductions.

FIGS. 1-6 illustrate various embodiments of five and six-axis,bi-tetrahedral mechanisms constructed in accordance with teachings ofthe invention.

FIG. 1 is a perspective view of a bi-tetrahedral parallel kinematicsmechanism having five prismatic actuators and first and secondconcentric spherical joint assemblies that are linked by a rigidintermediate limb. The embodiment includes one revolute actuator whichis mounted to a fixed base with a telescopic spline shaft assembly forrotationally driving an end-effector or work tool with six degrees offreedom.

FIG. 2 is a perspective view of another bi-tetrahedral parallelkinematics mechanism having a revolute actuator mounted to the secondconcentric spherical joint assembly for rotationally driving anend-effector or work tool with six degrees of freedom.

FIG. 3 is a perspective view of a bi-tetrahedral parallel kinematicsmechanism with a prismatic actuator linked as an intermediate limbbetween the first and second concentric spherical joint assemblies formoving a work tool with six degrees of freedom.

FIG. 4 is a perspective view of a bi-tetrahedral parallel kinematicsmechanism with a rigid intermediate limb linking the first and secondconcentric spherical joint assemblies for moving a work tool with fivedegrees of freedom.

FIG. 5 is a perspective view of a bi-tetrahedral parallel kinematicsmechanism having a revolute actuator as an intermediate limb linking thefirst and second joint assemblies for rotating the end-effector with sixdegrees of freedom.

FIG. 6 is a perspective view of a bi-tetrahedral parallel kinematicsmechanism having a revolute actuator mounted to the base, a spline shaftassembly driven by the revolute actuator, a first concentric sphericaljoint assembly having a revolute joint therein for transmittingrotational motion from the spline shaft assembly through a rotatableshaft as an intermediate limb linking the first and second concentricspherical joint assemblies for moving the end-effector with six degreesof freedom.

FIGS. 7-10 illustrate various four-axis, tetrahedral mechanismsconstructed in accordance with teachings of the invention with aconcentric spherical joint assembly for moving an end-effector.

FIG. 7 is a perspective view of a four degree of freedom tetrahedralmechanism which includes three piston-cylinder prismatic actuator limbs,a concentric spherical joint assembly, and one revolute actuator mountedto movable joint assembly for driving the end-effector or work tool.

FIG. 8 is a perspective view of a four degree of freedom tetrahedralmechanism with a revolute actuator fixedly mounted to the base fordriving the end-effector via a telescopic spline shaft assembly.

FIG. 9 is a perspective view of a four degree of freedom mechanismhaving three alternative slide-and-track type prismatic actuator limbsand a revolute actuator mounted to the movable joint assembly fordriving the end-effector.

FIG. 10 is a perspective view of a four degree of freedom mechanismhaving three alternative elbow-linkage revolute actuator limbs and arevolute actuator mounted to the movable joint assembly for driving theworking member.

FIG. 11 is a perspective view of a concentric spherical joint assemblyconstructed in accordance with teachings of the invention, the jointhaving a joint body, three elbows each having a proximal end pivotablymounted to the body by a respective revolute joint and a distal end witha respective revolute joint for mounting to limbs. The axes of rotationof the respective revolute joints intersect at a point.

FIG. 12 is a perspective view of the joint assembly of FIG. 11 shownwith the elbows in a different orientation.

FIG. 13 is a perspective view of another embodiment of a concentricspherical joint assembly constructed in accordance with teachings of theinvention, and as used in the embodiment of FIGS. 6, 7, 8, 9 and 10, thejoint body having a central revolute joint.

FIG. 14 is a perspective view of another embodiment of a concentricspherical joint constructed in accordance with teachings of theinvention, and as used in the mechanism of FIG. 1, the joint assemblyhaving three elbows and further having a universal joint connectormounted to the joint body, the center of the universal joint beingcoincident with the point of intersection of the axes of all proximaland distal revolute joints.

FIG. 15 is a perspective view of another embodiment of a concentricspherical joint assembly constructed in accordance with teachings of theinvention, and as used in the mechanism of FIG. 1, the joint assemblyincluding three elbows, one of the elbows being rigidly connected to acentral end component via a rigid component extending through the jointbody.

FIG. 16 is a perspective view of another embodiment of a concentricspherical joint assembly constructed in accordance with teachings of theinvention, and as used in the mechanism of FIGS. 3-6, the joint assemblyhaving two elbows and a central end component mounted to the joint bodyby revolute joints.

FIG. 17 is a perspective view of another embodiment of a concentricspherical joint assembly constructed in accordance with teachings of theinvention, the joint assembly including six elbows connecting six limbs.

FIG. 18 is a perspective view of another embodiment of a concentricspherical joint assembly constructed in accordance with teachings of theinvention, the joint assembly including nine elbows connecting ninelimbs.

FIG. 19 is a perspective view of an alternative actuator limb embodimenthaving a slide-and-track type prismatic structure.

FIG. 20 is a perspective view of an alternative actuator limb embodimenthaving an elbow linkage structure.

FIG. 21 is a perspective view of an alternative actuator limb embodimenthaving a ball-and-socket structure.

FIG. 22 is a perspective view of a true three-three Stewart platformincluding six concentric spherical joint assemblies constructed inaccordance with teachings of the invention.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

Now referring to the drawings, wherein like numerals designate likecomponents, FIG. 1 shows a five-axis parallel kinematics mechanism 100constructed in accordance with teachings of the present invention.Mechanism 100 includes a fixed base 1 and is operable to move andposition an end component 50 in space relative to the base 1 with fivedegrees of freedom. In an embodiment, an end-effector or work tool 60mounted to the end component 50 can be moved and positioned in spacerelative to the base 1 with six degrees of freedom. The position andorientation of the end component 50 are determined by five actuators A1,A2, A3, A4, and A5, as will be described.

As illustrated in FIG. 1, mechanism 100 includes a first tetrahedralstructure formed by first, second, and third actuator limbs A1, A2, A3each of which is mounted to the base 1 by a respective universal joint2. Specifically, in the embodiment illustrated, each of actuator limbsis a prismatic device, having a respective first limb member 3, secondlimb member 4, and an elbow 10. Upon actuation of a respective actuatorlimb, the first limb member 3 and second limb member 4 move relative toeach other for selectively extending or retracting the actuator limbalong an axis. The first limb member 3 is pivotably connected relativeto the base 1 by the respective universal joint 2. As illustrated, theactuator limbs A1-A5 are a telescopic piston-cylinder device, the firstlimb member 3 being a hydraulic cylinder and the second limb member 4being a piston. It should be understood that the actuator limbs couldalso be some other type of actuator device, such as a sliding-trackmechanism (e.g., FIG. 19), an elbow mechanism (e.g., FIG. 20), or apiston-cylinder device mounted on a ball-and-socket joint (e.g., FIG.21). Further, the prismatic actuation achieved by the piston cylinderarrangement could be substituted by alternative arrangements such as alinear motor, a ball screw-nut mechanism, a rack and pinion mechanism,or any other kind of a linear actuator.

The respective second limb members of actuator limbs A1, A2, A3 arepivotably connected to the elbows by means of revolute joints 11allowing the elbows one rotational degree of freedom with respect to thesecond limb members about a limb axis. It should be understood that therevolute joint 11 between elbow 10 and second limb member 4 could bereplaced by a revolute joint between first limb member 3 and universaljoint 2, allowing same rotational and translational freedom of elbow 10with respect to the base (this alternative location of revolute joint 11is not shown). Further, in such a case same said revolute joint anduniversal joint 2 could be replaced by a ball and socket joint (FIG.21).

The respective elbows 10 of actuator limbs A1, A2, A3 are mounted to afirst joint body 15 such that the elbows 10 and the first joint bodytogether make up a first concentric spherical joint assembly J1, asshown by way of example in FIG. 1. Each of the second limb members 4 hastwo non-actuated rotational and one actuated translational degree offreedom whereas each of the elbows has three non-actuated rotational andone actuated translational degree of freedom relative to base 1.

Referring also to FIG. 14, the first assembly J1 is shown in greaterdetail. The first joint assembly J1 connects together three limbs A1,A2, A3 of the mechanism 100 with a geometry that eventually facilitatesa closed-form solution for the forward kinematics. The joint assembly J1includes a central joint body 15. In the illustrated embodiment, thejoint body 15 is generally annular and frustoconical in shape. The jointassembly J1 also includes three pivotable elbows 10 mounted to the body15 with respective proximal revolute joints 12. A distal revolute joint11 is also provided at an opposite end of each elbow 10, by which elbow10 is mounted to the second limb member 4 of a respective one of theactuator limbs A1, A2, A3.

According to an embodiment of the invention, the axes of all sixrevolute joints 11, 12 in the first concentric spherical joint assemblyJ1 intersect at a point P1, as shown in FIG. 14. This configurationallows the second limb members of the limbs A1, A2, and A3 to rotateabout any axis passing through the point P1 independently of each other.The first joint body 15 has three degrees of freedom with respect to thebase 1. The position of the joint body 15 is defined by the state of thethree actuator assemblies A1, A2, A3.

As shown in FIG. 1, the mechanism 100 also includes a second tetrahedralstructure formed by fourth and fifth actuator limbs A4, A5, a secondconcentric spherical joint assembly J2 with a second joint body 215, andan intermediate limb mounted to link the first joint body 15 and thesecond joint body 215 of the respective joint assemblies J1 and J2 .Thus, the mechanism 100 is generally of a bi-tetrahedral structure.

Similarly to the first, second, and third actuator limbs A1, A2, and A3,the fourth and fifth actuator limbs A4, A5 each has a first limb member3 connected to the base 1 by a universal joint 2, an extendible secondlimb member 4 as well as a pivotably mounted elbow 10.

The elbows 10 of the two actuator limbs A4, A5 are mounted to a secondjoint body 215 such that the elbows 10, 210, and the second joint bodytogether make up a second joint assembly or second concentric sphericaljoint assembly J2. Still referring to FIG. 1, the kinematics mechanism100 includes an intermediate limb 41 which links the first joint body 15and the second joint body 215 of the respective joint assemblies J1 andJ2. The intermediate limb 41 is connected to the first joint body 15 bya universal joint 21, which has its center of rotation at point P1 (FIG.14). The intermediate limb 41 is connected to the second concentricspherical joint assembly J2 by a revolute joint 211 allowing rotationabout the longitudinal axis of the rigid member 41.

Referring to FIG. 15, the second joint assembly J2 is shown in greaterdetail. Like the first joint assembly J1, the illustrated embodiment ofthe joint assembly J2 has a joint body 215 and three elbows, includingtwo elbows 10, as described above in connection with joint assembly J1,and one elbow 210. Elbows 10 are rotatably mounted to the joint body 215with respective proximal revolute joints 12, and the elbow 210 isrotatably mounted to the joint body 215 with a proximal revolute joint212. Elbows 10 have a distal revolute joint 11 for further connecting tomembers or limbs. Elbow 210 also has a distal revolute joint 211 bywhich the elbow can be mounted to the intermediate limb 41, asillustrated in FIG. 1. The axes of all six revolute joints 11, 211, 12,and 212 in the concentric spherical joint assembly J2 intersect at apoint P2 allowing the actuator limbs and the intermediate limb 41 torotate about any axis passing through the point P2 independently of eachother.

As shown in FIG. 15, the elbow 210 is rigidly connected to the endcomponent 50, which movably resides within a central opening of thesecond joint body 215. More specifically, a portion 213 of the elbow 210extends through the revolute joint 212 into the joint body 215 and isrigidly connected to end component 50. In this configuration, the secondjoint body 215 has four degrees of freedom with respect to the base 1,and the end component 50 has five degrees of freedom with respect to thebase 1. The position of the end component 50 is defined by the state ofall five actuator assemblies A1, A2, A3, A4, and A5.

The end component 50 always maintains the same orientation relative to alimb (e.g. the intermediate limb 41 in FIG. 1) which is connected toelbow 210 by distal revolute joint 211, except for the rotationalorientation about the distal revolute joint 211. The usefulness of thisembodiment is that the limb which is attached to the elbow 210 cancontrol two orientations of end component 50. In contrast, limbs (e.g.the second members 4 of actuator limbs A4, A5 in FIG. 1) connected tothe other two elbows 10 are each only capable of controlling oneorientation of the end component 50.

It should be understood that the universal joint 21 and the distalrevolute joint 211 could be substituted by a ball-and-socket joint 269connecting the intermediate limb 41 to joint body 15, as shown in FIG.2. In such a case, the intermediate limb would be rigidly mounted to theelbow 210.

Referring back to FIG. 1, the end component 50 can support anend-effector or work tool 60, such as a gripper, a welding device, adrill or milling device, a cutting tool, a press element, a sensor orany other kind of end-effector. Additionally, such a work tool 60 couldbe mounted to the end component 50 by a further revolute joint, therebyallowing the work tool 60 six degrees of freedom. In the illustratedembodiment, work tool 60 is rotationally driven by a motor 31 mounted tothe base 1, the motor 31 transmitting power through a telescopic splineshaft assembly S to the work tool 60.

As shown, the spline shaft assembly S includes two universal joints 33a, 33 b connected by a sleeve 34 and a spline shaft 35 allowing torquetransmission between the two non-parallel and non-intersecting axes ofthe motor 31 and the work tool 60. The actuator assemblies A1, A2, A3,A4, A5 form kinematic loops through the spherical joint assemblies J1and J2 thus giving the mechanism 100 its parallel kinematiccharacteristics.

It should be understood that the mechanism 100, and other mechanismsdescribed herein, may be controlled by one or more computers (notshown). The computer is operable to controllably move the mechanism, andthe computer can instruct the actuator limbs to move in a desiredmanner. In a generally known manner, the computer receives variousfeedback inputs which indicate the position and status of the mechanism,such as signals transmitted from sensors located at the respectiveactuators. From this actuator position information, the computer cancalculate the position and orientation of the end-effector, as isgenerally known in the art. This type of calculation is generally knownas forward kinematics. The advantageous design of the concentricspherical joint disclosed herein facilitates a closed-form solution tothis forward kinematics calculation, as will be recognized by thoseskilled in the art. This enables greatly simplified mathematics andfaster processing by the computer.

Turning to FIG. 2, another mechanism 200 is shown. The embodiment ofFIG. 2 is similar to the embodiment of FIG. 1, except that mechanism 200has a motor 37 mounted to the end component 50 of the second concentricspherical joint assembly J2 for rotating a work tool 61 rotatablymounted to the end component 50.

FIG. 3 illustrates a further mechanism 300 for positioning and orientinga member in space with six degrees of freedom. The mechanism 300 issimilar to the embodiments of FIGS. 1 and 2, except that the mechanism300 of FIG. 3 includes a prismatic device such as an intermediateactuator limb 341 which is mounted to link the joint body 15 of thefirst joint assembly J1 to a joint body 315 of a second concentricspherical joint assembly J3, instead of the rigid member 41 of FIG. 2.Moreover, the second joint assembly J3 has a different configurationthan the joint assembly J2 illustrated in FIGS. 1 and 2. Joint assemblyJ3 is illustrated in greater detail in FIG. 16.

The intermediate actuator limb 341 includes a first member 42 which ismounted to the body 15 of the first joint assembly J1 by a universaljoint 21, as illustrated in FIG. 3. The actuator limb 341 also includesa second member 43 which is mounted to an end component 350 of theconcentric spherical joint J3 by means of a revolute joint 355 (FIG. 16)that permits the rotation of the second member 43 of the intermediateactuator limb 341 about a longitudinal axis of the intermediate actuatorlimb 341.

As illustrated in FIG. 16, the end component 350 is pivotally mountedcentrally within an opening of the joint body 315 by a pair of revolutejoints 360. The joint assembly J3 has two elbows 310, each being mountedto the joint body 315 by respective proximal revolute joints 312. Theintermediate actuator limb 341 is operable to selectively move the firstand the second joint bodies of respective joint assemblies J1 and J3relative to each other. In the embodiment shown in FIG. 16, the axis ofrotation of the end component 350 relative to the joint body 315 and theaxes of rotation of the elbows 310 relative to the joint body 315 arenon-parallel. All axes of the six revolute joints 311, 312, 355, and 360of the concentric spherical joint assembly J3 intersect at a point P3.Thus, the revolute joint 355 is analogous to the distal revolute joints311 and the revolute joints 360 are analogous to the proximal revolutejoints 312. The joint body 315 of joint assembly J3 has four degrees offreedom with respect to the base 1, whereas the end component 350 hasfive degrees of freedom with respect to the base 1. As illustrated inFIG. 3, a work tool 61 movably mounted to the end component 350 andrigidly connected to the second member 43 of the intermediate actuatorlimb 341 has six degrees of freedom.

Turning now to FIG. 4, a further mechanism 400 for positioning andorienting a member in space with five degrees of freedom is shown.Mechanism 400 represents a variation of the embodiment of FIG. 3,wherein the prismatic actuator limb 341 of the embodiment of FIG. 3 hasbeen replaced with a rigid intermediate limb 44. An end of theintermediate limb 44 is mounted to the universal joint 21 on the jointbody 15 of the first concentric spherical joint assembly J1. An oppositeend of the intermediate limb 44 is mounted to the revolute joint 355(FIG. 16) on the end component 350 of the concentric spherical jointassembly J3, allowing rotation about the longitudinal axis of therevolute joint. A work tool 61 is mounted to the rigid intermediate limb44 and has five degrees of freedom.

A further embodiment is illustrated in FIG. 5, showing a mechanism 500for positioning and orienting a member in space with six degrees offreedom. Mechanism 500 is generally similar to the embodiment of FIG. 3,but has a revolute actuator 541 linking joint body 15 of the first jointassembly J1 to joint body 315 of the second joint assembly J3, insteadof the prismatic actuator 341 of the mechanism 300 in FIG. 3. Therevolute actuator 541 of mechanism 500 has a first member 38,illustrated as a motor, and a second member 39, illustrated as a shaft.The revolute actuator 541 is actuatable to cause rotation of the secondmember 39 relative to the first member 38. The first member 38 ismounted to joint body 15 of the first joint assembly J1 by the universaljoint 21. The second member 39 is connected to the end component 350 ofthe second joint assembly J3 by means of the revolute joint 355, therebyallowing rotation about the longitudinal axis of the revolute actuator541. A work tool 60 is driven by the rotation of member 39 and has sixdegrees of freedom.

Referring to FIG. 6, an alternative mechanism 600 for positioning andorienting a member in space with six degrees of freedom is shown. Theembodiment of FIG. 6 is similar to the embodiment of FIG. 5, but themechanism 600 has a concentric spherical joint assembly or first jointassembly J4 which includes a central revolute joint 416 (FIG.13)allowing rotation of the intermediate limb 44 about a central axispassing through the point P4 (FIG. 13), as a rotary shaft for rotatingthe work tool 61 mounted to the second joint assembly J3. The mechanism600 includes a motor 631 mounted to the base 1. A spline shaft assemblyS6 is connected between the motor 631 and the first joint assembly J1.Through the spline shaft assembly S6, the motor 631 transmits power tothe work tool 60, passing through joint body 415. The spline shaftassembly S6 has a universal joint 633 a, which drives female and malespline shaft members, 634 and 635, respectively. Another universal joint633 b connects the spline member 635 to the universal joint 21, therebyrotating the central revolute joint 416 (FIG. 13) inside joint body 415of the joint assembly J4. The intermediate shaft 44 is then rotationallydriven through the universal joint 21. The shaft 44 is mounted to rotatethe work tool 61, thereby providing the work tool 61 with six degrees offreedom.

FIGS. 7-10 illustrate various tetrahedral kinematics mechanisms forproviding four degrees of freedom, useful for purposes of free formmachining as well as other positioning and orienting devices requiringlimited degrees of freedom. Referring to FIG. 7, a mechanism 700 isshown which has three prismatic actuator limbs A1, A2, A3 mounted to abase 1, the actuator limbs A1, A2, A3 being also mounted to a joint body415 of a concentric spherical joint assembly J4, as described above inconnection with FIGS. 1 and 6, forming a tetrahedral structure. Each ofthe limbs A1, A2, A3 is mounted to the base 1 with a universal joint 2.The mechanism 700 includes a motor 47 mounted to the body 415 of theconcentric spherical joint assembly J4. The motor 47 has three degreesof freedom with respect to the base 1. The mechanism 700 also includesan end-effector or work tool 61 that is mounted to the motor 47 and canbe positioned and oriented in space with four degrees of freedom. Thejoint assembly J4 is shown in greater detail in FIG. 13. The actuatorassemblies A1, A2, A3 form kinematic loops through the concentricspherical joint assembly J4 thus making the mechanism 700 a trulyparallel kinematic mechanism.

Referring to FIG. 8, an alternative mechanism for positioning andorienting a member in space with four degrees of freedom is shown. Thisis constructed similarly to the embodiment of FIG. 7, but, as in theembodiment described in connection with FIG. 6, a motor 31 and a splineshaft assembly S6 may be provided to rotate the work tool 60 ofmechanism 800. The body 415 of the joint assembly J4 includes a revolutejoint 416 (FIG. 13) which connects between the work tool 60 and thespline shaft assembly S6 to allow rotation. The spline shaft assembly S6includes two universal joints 633 a and 633 b connected by a sleeve 634and a spline shaft 635, allowing transmission of rotational motionbetween the two non-parallel and non-intersecting axes of the motor 31and the work tool 60. The joint body 415 has three degrees of freedomwith respect to the base 1 whereas the work tool 60 has four degrees offreedom with respect to the base 1.

Illustrating the implementation of alternative types of actuator limbs,the embodiment of FIG. 9 illustrates a mechanism 900 having a base 1 andend-effector or work tool 60 which can be positioned and oriented inspace with four degrees of freedom. The embodiment of FIG. 9 includesthree actuator limbs A9 of a slide-and-track type. More particularly, asseparately illustrated in FIG. 19, each actuator limb A9 has a track 5fixedly mounted to the base 1, an actuatable prismatic slider 6 which isslidably mounted to the track 5 and a rigid member 8 linking the slider6 to the joint assembly J4. The rigid member 8 has a first end mountedto the slider 6 with a universal joint 7. As shown in FIG. 9, theactuator limbs also include an elbow 10 which is mounted to the rigidmember 8 by a distal revolute joint 11 to allow rotation of the elbow 10about a limb axis. The elbows 10 are rotatably mounted to the joint body415 using the proximal joints 12 allowing rotation about a proximalaxis. Each of the rigid members 8 has two non-actuated rotational andone actuated translational degree of freedom whereas each of the elbows10 has three non-actuated rotational and one actuated translationaldegree of freedom. In this embodiment, the mechanism 900 does notsupport the weight of the prismatic sliding track actuator components 5and 6 and hence the mechanism 900 has light weight and yields high speedperformance. This also applies to the aforementioned five and six axismechanisms when replacing the prismatic devices in the actuator limbsshown in FIG. 1-6 by a similar slide-and-track device.

FIG. 10 illustrates a tetrahedral parallel kinematics mechanism 1000having three actuator limbs A10 each having an elbow configuration. Themechanism 1000 is capable of positioning the work tool 60 with fourdegrees of freedom.

More specifically, as separately illustrated in FIG. 20, each actuatorlimb A10 has a revolute actuator 91 mounted to the base 1 and anactuator shaft 92. The revolute actuator 92 pivots a first rigid member99 connected to the shaft 92. A second rigid member 98 has a first endwhich is movably mounted to the first rigid member 99 by a universaljoint 97. As shown in FIG. 10, each actuator limb A10 also comprises anelbow 10 which is mounted to the second end of rigid member 98 by adistal revolute joint 11. The second rigid member 98 of each of theactuator limbs A10 has two non-actuated rotational and one actuatedrotational degree of freedom whereas the elbows 10 have threenon-actuated rotational and one actuated translational degree offreedom. In this embodiment, the weight of the revolute actuators 91 issupported directly by base 1, not by the movable components of themechanism 1000, thereby facilitating light weight and high speedperformance. This is again true for the aforementioned five and six axismechanisms when replacing the prismatic devices in the actuator limbsshown in FIG. 1-6 by a similar elbow configuration or elbow linkagedevice. Revolute actuators are typically inexpensive, so the embodimentof FIG. 10 is cost effective.

Referring to FIG. 11, a concentric spherical joint J5 constructedgenerally in accordance with teachings of the invention and which may beused in the aforementioned kinematics mechanisms is shown. Theconcentric spherical joint mechanism J5 includes a circular body 18 andthree proximal revolute joints 12, to which three elbows 10 arepivotably mounted. The revolute joints allow rotation of the elbows 10relative to the body 18 about the longitudinal axis of the respectiverevolute joints 12. This axis will be referred to as a joint axis. Eachelbow also has a distal revolute joint 11 for connecting to a respectivelimb, allowing rotation about an axis of the respective revolute joint11 or limb axis. Each limb axis is non-parallel relative to the jointaxis of the same elbow 10. The axes of all six revolute joints 11, 12i.e. the joint axes and the limb axes intersect at a point P5. As aresult of this geometry, members or limbs connected to elbows 10 by thedistal revolute joints 11 can rotate independent of each other about anyaxis passing through the intersection point P5. Members or limbsconnected to distal revolute joints 11 of the concentric spherical jointassembly J5 behave as if they were connected to each other by means ofconventional concentric spherical joints such as ball and socket joints.For example, such a member could be the second member 4 of the actuatorlimbs A1 to A5 shown in FIG. 1.

Demonstrating that the point P5 is invariant with respect to theorientations of the elbows 10, FIG. 12 shows the joint assembly J5 withthe elbows in a different orientation than illustrated in FIG. 11. Ascan be seen from FIG. 12, all of the axes of the revolute joints 11 and12 still meet at the point P5, although the elbows 10 are in anasymmetric position.

Referring to FIG. 13, a modification J4 of the same concentric sphericaljoint J5 of FIG. 11 is shown. In addition, a member can be attached by arevolute joint 416 passing through the center of the joint body 415 suchthat the axis of the revolute joint 416 passes through the intersectionpoint P4. This has been used in many of the aforementioned parallelkinematics mechanisms.

Referring to FIG. 14, the previously described joint assembly J1 isshown in detail. The universal joint 21 is shown mounted to the jointbody 15. The universal joint 21 has two axes of rotation which intersectat a common point P1, coincident with the point of intersection of theaxes of rotation of the six other revolute joints 11, 12 of the jointassembly J1. The universal joint 21 is mounted to a plate 21 a and astud 21 b for connecting to further members or limbs such as member 41shown in FIG. 1.

As an alternative to the joint assembly J1 shown in FIG. 14, a revolutejoint added between plate 21 a and stud 21 b could be used to allowrotation of stud 21 b relative to plate 21 a about an axis passingthrough P5. Thus, members connected to the distal revolute joints 11 andthe rotatable stud 21 b can rotate independent of each other about anyaxis passing through the point P5. Members connected to the distalrevolute joints 11 and the rotatable stud 21 b behave as if they wereconnected to each other by means of conventional concentric sphericaljoints such as ball and socket joints.

To enable the connection of six limbs, FIG. 17 illustrates a concentricspherical joint assembly J17 which is constructed by connecting togetherthe concentric spherical joint assemblies J4 and J1, described above inconnection with FIGS. 13 and 14, respectively. The revolute joint 416inside joint body 415 of joint assembly J4 is rigidly mounted to stud 21b of joint assembly J1 (FIG. 14), allowing joint body 415 threerotational degrees of freedom with respect to joint body 15. Inaccordance with an embodiment of the invention, the axes of all twelverevolute joints 11, 12 of the joint assembly J17 as well as the centerof rotation of the universal joint 21 intersect at the same pointirrespective of the orientations of all individual members. Thus,members or limbs connected to the distal revolute joints 11 can rotateindependently of each other about any axis passing through the centerpoint, allowing the mechanism the same freedom as six ball joints with acommon center point. The joint assembly J17 is useful, for example, in atruss structure for distributing loads among six limbs without causingany bending or twisting moments on limbs connected to the distalrevolute joints 11.

For joining nine limbs, FIG. 18 illustrates a concentric spherical jointassembly J18 wherein three satellite concentric spherical jointassemblies J8 are mounted to the respective distal revolute joints 11 ofthe centrally positioned concentric spherical joint assembly J4,previously described independently in connection with FIG. 13. Moreparticularly, each of the satellite joint assemblies J8 includes asatellite joint body 815, three satellite elbows 810 having proximalends rotatably mounted to the satellite joint body 815 by respectiverevolute joints 812. Each satellite elbow 810 also has a distal endhaving a revolute joint 811 for attaching to a satellite limb (notshown). The axes of rotation of all twenty four revolute joints 11, 12,811, 812 intersect at a common point. Thus, members or limbs connectedto the nine distal revolute joints 811 of the three satellite concentricspherical joint assemblies J8 can rotate independent of each other aboutany axis passing through the common point, thereby allowing the jointassembly J18 the same freedom as nine ball joints with a common centerpoint. The joint assembly J18 is useful, for example, in a trussstructure for distributing loads among nine limbs. This embodimentillustrates continuous stacking of satellite joint assemblies toincrease the number of limbs rotating about a single common point aswell as having complete orientational independence.

FIG. 21 shows an alternative type of prismatic actuator limb A21, whichmay be used in the aforementioned parallel kinematics mechanismsutilizing the concentric spherical joint described herein in accordancewith the invention. The actuator limb A21 includes a ball 96 which ismountable to a fixed base and a socket 95 which is pivotable on the ball96. The socket 95 is connected to a prismatic cylinder 93 operablyassembled with a piston 94, giving the piston 94 three rotationaldegrees of freedom and an actuated translational degree of freedom. Whenused as in conjunction with the aforementioned parallel kinematicsmechanisms, the actuator limb would also include an elbow (not shown inFIG. 21) mounted to piston 94 in a manner similar to that described inconnection with elbow 10 shown in FIG. 1.

The concentric spherical joint assembly disclosed herein can be used toimprove otherwise known geometric kinematic structures. The intersectingaxes facilitate simpler and direct kinematics solutions. For example, asillustrated in FIG. 22, a mechanism 2200 is based on a three-threeStewart Platform design, which includes concentric spherical jointassemblies J5 (FIG. 11), which are easy to manufacture and work with.The mechanism 2200 includes a base 70 and a movable end member 71 whichcan be positioned and oriented in space with six degrees of freedom. Oneof the distal revolute joints 11 of three respective concentricspherical joint assemblies J5 is mounted to the base 1. The remainingtwo elbows 10 of each of these base-mounted joint assemblies J5 are eachrespectively connected to a prismatic actuator limb A by the distalrevolute joints 11. The movable end member 71 is similarly connected todistal revolute joints 11 of one of the elbows 10 of three additionalconcentric spherical joint assemblies J5. The remaining two elbows 10 ofeach of these joint assemblies J5 mounted to the end member 71 areconnected to the opposite ends of the prismatic actuator limbs A, suchthat two elbows 10 of each base-mounted joint assembly J5 are linked totwo elbows 10 of two separate movable-end-member-mounted jointassemblies J5.

Although the invention has been described herein in connection withvarious preferred embodiments, there is no intention to limit theinvention to those embodiments. It should be understood that variouschanges and modifications to the preferred embodiments will be apparentto those skilled in the art. Such changes and modifications may be madewithout departing from the spirit and scope of the present invention andwithout diminishing its attendant advantages. Therefore, the appendedclaims are intended to cover such changes and modifications.

What is claimed is:
 1. A mechanism for positioning and orienting an endcomponent in space with at least five degrees of freedom, the mechanismcomprising: a base; at least first, second, third, fourth, and fifthactuator limbs, each of the actuator limbs including at least a firstlimb member pivotably mounted to said base, a second limb member movablyconnected to the first limb member, and an elbow movably connected tothe second limb member, wherein the elbow has at least four degrees offreedom relative to said base, at least one of said degrees of freedomof the elbow being actuatable relative to the base, and wherein at leastthree of the degrees of freedom of the elbow are free, including onefree rotational degree of freedom about a respective limb axis; a firstjoint body, the elbows of said first, second, and third actuator limbseach being mounted to said first joint body such that the first, second,and third actuator limbs are each movable relative to said first jointbody about a respective joint axis which is non-parallel to the limbaxis of the respective actuator limb, wherein the joint axes of saidfirst joint body and the limb axes of the first, second, and thirdactuator limbs intersect at a first common point; a second joint body,the elbows of said fourth and fifth actuator limbs each being mounted tosaid second joint body such that the fourth and fifth actuator limbs areeach movable relative to the second joint body about a respective jointaxis which is non-parallel to said limb axis of the respective actuatorlimb, wherein the joint axes of said second joint body and the limb axesof the fourth and fifth actuator limbs intersect at a second commonpoint; and an end component movably mounted to said second joint body,the end component being movably connected to said first joint body suchthat said end component is movable with three degrees of freedomrelative to the first joint body and five degrees of freedom relative tosaid base.
 2. A mechanism according to claim 1, wherein said endcomponent rotates relative to said second joint body about an axis whichintersects said second common point.
 3. The mechanism according to claim1, further comprising an intermediate limb having opposite first andsecond ends and an intermediate axis extending between the first andsecond ends, the first end being movably mounted to said first jointbody and the second end being movably mounted to said end component by arevolute joint to allow rotation of said intermediate limb relative tosaid end component about said intermediate axis.
 4. A mechanismaccording to claim 3, wherein said intermediate axis intersects saidfirst common point.
 5. A mechanism according to claim 3, wherein saidintermediate axis intersects said second common point.
 6. A mechanismaccording to claim 3, further comprising a universal joint connectingsaid first joint body to said intermediate limb, wherein the universaljoint includes two revolute joints with non-parallel axes intersectingat a center point.
 7. A mechanism according to claim 6, where saidcenter point is coincident with said first common point.
 8. A mechanismaccording to claim 1, wherein the end component is connected to saidfirst joint body with a ball-and-socket joint having a center point. 9.A mechanism according to claim 8, where said center point is coincidentwith said first common point.
 10. A mechanism according to claim 1,further comprising a revolute joint connecting the elbow of one of saidactuator s to the respective joint body for relative rotation about ajoint axis.
 11. A mechanism according to claim 1, further comprising aplurality of universal joints, each of said universal joints pivotablyconnecting the first limb member of a respective one of said first,second, third, fourth and fifth actuator limbs to said base, each ofsaid universal joints including two revolute joints with non-parallelaxes intersecting at a base point, a plurality of actuated prismaticjoints connecting the first limb member to the second limb member, and aplurality of revolute joints rotatably connecting the second limb memberto the elbow of each respective actuator limb allowing rotation of theelbow about said limb axis.
 12. A mechanism according to claim 11,wherein said limb axis intersects a base point axis.
 13. A mechanismaccording to claim 1, further comprising a plurality of universaljoints, each of said universal joints pivotably connecting the firstlimb member of a respective one of said first, second, third, fourth andfifth actuator limbs to said base, each of said universal jointsincluding two revolute joints with non-parallel axes intersecting at abase point, a plurality of revolute joints rotatably connecting thefirst limb member to the second limb member allowing rotation of thesecond limb member about said limb axis, and a plurality of actuatedprismatic joints connecting the second limb member to the elbow of eachrespective actuator limb.
 14. A mechanism according to claim 13, whereinsaid limb axis intersects a base point axis.
 15. A mechanism accordingto claim 1, further comprising at least one ball-and-socket jointpivotably connecting the first member of at least one of said actuatorlimbs to the base.
 16. A mechanism according to claim 1, wherein atleast one of said actuator limbs is an elbow linkage device comprisingsaid first limb member rotatably connected to the base by an actuatedrevolute joint, the first limb member pivotably connected to a secondlimb member by a universal joint and the second limb member rotatablyconnected to the elbow by a revolute joint allowing rotation about saidlimb axis.
 17. A mechanism according to claim 1, further comprising awork tool rotatably mounted to said end component for actuatablemovement relative thereto.
 18. A mechanism according to claim 17,further comprising a motor mounted to said base and a shaft assemblyoperably linking said motor to said work tool, the motor driving saidwork tool to rotate.
 19. A mechanism according to claim 17, furthercomprising a motor mounted to said end component and operably linked tosaid work tool, the motor driving said work tool to rotate.
 20. Amechanism according to claim 3, wherein said intermediate limb is aprismatic actuator for moving first and second joint body relatively toeach other.
 21. A mechanism according to claim 3, wherein saidintermediate limb is a revolute actuator with an actuatable shaft.
 22. Amechanism according to claim 21, further comprising a work tool rigidlymounted to said shaft of the revolute actuator.
 23. A mechanismaccording to claim 3, further comprising a motor mounted to said baseand a shaft assembly operably linking said motor to said intermediatelimb, the motor driving said intermediate limb to rotate about saidintermediate axis.
 24. A mechanism according to claim 23, wherein theintermediate limb is mounted to a universal joint which includes tworevolute joints whose axes are non-parallel to said intermediate axis,with the universal joint being connected to the first joint body by arevolute joint allowing rotation about a central axis.
 25. A mechanismaccording to claim 23, further comprising a work tool rigidly mounted tosaid intermediate limb.
 26. A mechanism for positioning and orienting ajoint body in space with at least three degrees of freedom, themechanism comprising: a base; at least first, second, and third actuatorlimbs, each of the actuator limbs including a first limb memberpivotably mounted to said base, a second limb member movably connectedto the first limb member, and an elbow movably connected to the secondlimb member, wherein the elbow has at least four degrees of freedomrelative to said base, at least one of said degrees of freedom of theelbow being actuatable relative to the base, and wherein at least threeof the degrees of freedom of the elbow are free, including one freerotational degree of freedom about a respective limb axis; and a jointbody, the elbows of said first, second, and third actuator limbs eachbeing mounted to said joint body such that the first, second, and thirdactuator limbs are each movable relative to said joint body about arespective joint axis which is non-parallel to the limb axis of therespective actuator limb, wherein the joint axes of said first jointbody and the limb axes of the first, second, and third actuator limbsintersect at a common point; and a plurality of universal joints, eachof said universal joints pivotably connecting the first limb member of arespective one of said actuator limbs to said base, each of saiduniversal joints including two revolute joints with non-parallel axesintersecting at a base point, a plurality of actuated prismatic jointsconnecting the first limb member to the second limb member, and aplurality of revolute joints rotatably connecting the second limb memberto the elbow of each respective actuator limb allowing rotation of theelbow about said limb axis.
 27. A mechanism according to claim 26,wherein said limb axis intersects a base point axis.
 28. A mechanismaccording to claim 26, further comprising a work tool rotatably mountedto said joint body for actuatable movement relative thereto.
 29. Amechanism according to claim 20, further comprising a motor mounted tosaid base and a shaft assembly operably linking said motor to said worktool, the motor driving said work tool to rotate.
 30. A mechanismaccording to claim 20, further comprising a motor mounted to said jointbody and operably linked to said work tool, the motor driving said worktool to rotate.